Large Deviation Principles for Stochastic Volatility Models with Reflection

We introduce and study time-inhomogeneous stochastic volatility models with reflection. In such models, the volatility is described by a nonnegative time-dependent function of a reflecting diffusion. The main results obtained in the present paper are sample path and small-noise large deviation principles for the log-price process in a model with reflection under rather mild restrictions. We use these results to study the asymptotic behavior of binary barrier options and call prices in the small-noise regime.